1. Field of the Art
The present invention relates to the field of digital transmission and more particularly to a method of adaptive blind equalization for the reception of electrical signals codified in symbols and transmitted on a transmission channel of unknown characteristics variable in time which introduces an intersymbol interference. The reception device uses a filter with adaptable parameters at the output of which there are signal samples, a decision element which assigns to each signal sample a symbol, and a control device. On the basis of a pilot vector of received signals, signal samples, and decided symbols adjustments are made to the adaptable parameters of the filter until an optimal configuration is reached which gives the least intersymbol interference.
2. Background of the Prior Art
In synchronous data transmission systems, because of the non-ideality of the frequency response of the transmission channels, each transmitted symbol interferes with the others, generating an intersymbol interference. To attenuate the intersymbol interference, the systems are usually equipped with equalizers (see Lucky R. W., "Automatic equalization for digital communication", Bell Syst. Tech. J., 1965, 44, pp. 574-588).
Such equalizers, referred to as transversal, are made with a chain of delay elements, at the output of each of which is placed a variable gain amplifier (tap gain). The tap gain outputs are then added to provide a signal sample which gives an indication of the transmitted symbol. This signal sample is then sent to a decision element to obtain a decided signal. Assuming no errors, the decided signal should be equal to the signal fed into the transmission channel.
By appropriate selection of the delay elements and the tap gains, transversal equalizers can reduce the intersymbol interference according to a given criterion. Some types of equalizers, referred to as adaptive, have an automatic tap gain control and adjustment system. In these equalizers, starting from arbitrary initial tap gain values, even quite far from the optimum, can be modified iteratively until an optimal configuration is reached and held by slow variations of the transmission channel characteristics.
To minimize intersymbol interference many adaptive (self-learning) equalization systems adopt the criterion of minimizing the mean square error (MSE) between the signal samples at the equalizer output before the decision and the corresponding transmitted signals using estimated gradient methods. For a given transmission channel, the mean square error is a quadratic function of the tap gains. The mean square error is minimized by estimating its gradient on the basis of the input sequence, the output sequence, and a transmitted reference sequence. The gains are modified in the direction opposite to the estimated gradient.
More particularly, starting from arbitrary tap gain values, differences are found between the transmitted reference symbols and the signal samples at the equalizer output. Using these differences, in combination with the signals present at the equalizer input, the tap gains are modified to obtain the minimum mean square error. It can be shown that a tap gain configuration which minimizes the mean square error exists and is unique (see Gersho A., "Adaptive equalization of highly dispersive channels for data transmission", Bell System Technical Journal, 1969, 48, pp. 55-70).
When the optimum configuration has been reached the outputs of the receiver decision element, i.e. the self-decided symbols, are correct with very high probability and can be used instead of the reference symbols to obtain the present value of the error to be used in the adaptation algorithm. The basic assumption for the adaptive equalizer is therefore that the current output samples for the adaptive equalizer can be compared with the corresponding transmitted symbols, which have to be known a priori. However, if the channel characteristics change during transmission, the self-decided symbols may become incorrect and the equalizer is unable to reconfigure the tap gains to the new optimum values. In this case, to obtain reliable self-decided symbols at the receiver output, the above described start-up procedure must be repeated with considerable loss of time.
To remedy this serious drawback, self-learning or adaptive blind equalization methods, i.e. capable of converging in a configuration of limited distortion without the necessity of using a predetermined reference symbol sequence, have been proposed (see Y. Sato, "A method of self-recovering equalization for multi-level amplitude-modulation systems", IEEE Transaction on Communication, Vol. COM-23, N. 6, pp. 679-682, June 1975; D. N. Godard, "Self-recovering equalization and carrier tracking in two-dimensional data communication systems", IEEE Transaction on Communication, Vol. COM-28, N. 11, pp. 1867-1875, November 1980; A. Benveniste and M. Goursat, "Blind equalizers", IEEE Transaction on Communication, Vol. COM-32, N. 8, pp. 871-883, August 1984).
Another benefit of the blind convergence method is that there is no need for preliminary carrier phase recovery but this recovery can be accomplished in the blind convergence period even if during this period the decided symbols are mostly incorrect.
To minimize intersymbol interference these methods use new non-convex cost functions different than the mean square error used for the self-learning equalizer. Under weak conditions, these cost functions characterize the intersymbol interference sufficiently well while their stochastic minimization can be performed by using locally generated control signals with no knowledge of the transmitted data.
However, these methods of adaptive blind equalization are not fully satisfactory because they do not converge smoothly, and particularly because under steady state operating conditions they maintain a very high residual variance of the error signal. In other words, they do not reach the point of minimal intersymbol interference but oscillate continually around the minimum. This leads to operation under unacceptable working conditions.